{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-04-09T12:27:22.321388Z",
     "start_time": "2025-04-09T12:27:22.201571Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义向量\n",
    "vector = np.array([4, 3])\n",
    "\n",
    "# 创建网格坐标\n",
    "grid_x, grid_y = np.meshgrid(np.arange(-5, 6), np.arange(-5, 6))\n",
    "\n",
    "# 绘制背景网格\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.grid(True, which='both', linestyle='--', linewidth=0.5, color='gray')\n",
    "plt.axhline(0, color='black', linewidth=0.8)\n",
    "plt.axvline(0, color='black', linewidth=0.8)\n",
    "plt.xlim(0, 5)\n",
    "plt.ylim(0, 5)\n",
    "\n",
    "# 绘制向量\n",
    "plt.quiver(0, 0, vector[0], vector[1], angles='xy', scale_units='xy', scale=1, color='black', label='向量')\n",
    "\n",
    "# 绘制 L1 范数的路径（蓝色）\n",
    "L1_path = [(0, 0), (vector[0], 0), vector]\n",
    "L1_x = [point[0] for point in L1_path]\n",
    "L1_y = [point[1] for point in L1_path]\n",
    "plt.plot(L1_x, L1_y, marker='o', color='blue', label='L1 范数')\n",
    " \n",
    "# 添加标题和图例\n",
    "plt.title('向量的范数示意图')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.legend()\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "\n",
    "# 显示图形\n",
    "plt.show()\n"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-09T12:27:41.502588Z",
     "start_time": "2025-04-09T12:27:41.393659Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义向量\n",
    "vector = np.array([4, 3])\n",
    "\n",
    "# 创建网格坐标\n",
    "grid_x, grid_y = np.meshgrid(np.arange(-5, 6), np.arange(-5, 6))\n",
    "\n",
    "# 绘制背景网格\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.grid(True, which='both', linestyle='--', linewidth=0.5, color='gray')\n",
    "plt.axhline(0, color='black', linewidth=0.8)\n",
    "plt.axvline(0, color='black', linewidth=0.8)\n",
    "plt.xlim(0, 5)\n",
    "plt.ylim(0, 5)\n",
    "\n",
    "# 绘制向量\n",
    "plt.quiver(0, 0, vector[0], vector[1], angles='xy', scale_units='xy', scale=1, color='black', label='向量')\n",
    "\n",
    " \n",
    "\n",
    "# 绘制 L2 范数的路径（红色）\n",
    "L2_path = [(0, 0), vector]\n",
    "L2_x = [point[0] for point in L2_path]\n",
    "L2_y = [point[1] for point in L2_path]\n",
    "plt.plot(L2_x, L2_y, marker='o', color='red', label='L2 范数')\n",
    "\n",
    "\n",
    "\n",
    "# 添加标题和图例\n",
    "plt.title('向量的范数示意图')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.legend()\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "\n",
    "# 显示图形\n",
    "plt.show()\n"
   ],
   "id": "aa857939b06371bb",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-09T12:29:41.112111Z",
     "start_time": "2025-04-09T12:29:41.001577Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义向量\n",
    "vector = np.array([4, 3])\n",
    "\n",
    "# 创建网格坐标\n",
    "grid_x, grid_y = np.meshgrid(np.arange(-5, 6), np.arange(-5, 6))\n",
    "\n",
    "# 绘制背景网格\n",
    "plt.figure(figsize=(8, 8))\n",
    "plt.grid(True, which='both', linestyle='--', linewidth=0.5, color='gray')\n",
    "plt.axhline(0, color='black', linewidth=0.8)\n",
    "plt.axvline(0, color='black', linewidth=0.8)\n",
    "plt.xlim(0, 5)\n",
    "plt.ylim(0, 5)\n",
    "\n",
    "# 绘制向量\n",
    "plt.quiver(0, 0, vector[0], vector[1], angles='xy', scale_units='xy', scale=1, color='black', label='向量')\n",
    "\n",
    " \n",
    "\n",
    "\n",
    "# 绘制 L∞范数的路径（绿色）\n",
    "Linf_path = [(0, 0), (vector[0], 0), (vector[0], vector[1]), vector]\n",
    "Linf_x = [point[0] for point in Linf_path]\n",
    "Linf_y = [point[1] for point in Linf_path]\n",
    "plt.plot(Linf_x, Linf_y, marker='o', color='green', label='L∞范数')\n",
    "\n",
    "# 添加标题和图例\n",
    "plt.title('向量的范数示意图')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.legend()\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "\n",
    "# 显示图形\n",
    "plt.show()\n"
   ],
   "id": "8d924bd52cc9055a",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-09T12:48:23.011046Z",
     "start_time": "2025-04-09T12:48:22.995047Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "556cc3501f907065",
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-09T12:48:23.199046Z",
     "start_time": "2025-04-09T12:48:23.186827Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "3a44c66554727f8a",
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-09T12:48:23.324792Z",
     "start_time": "2025-04-09T12:48:23.320791Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "4d82d72eaffd6afb",
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-09T12:48:40.177735Z",
     "start_time": "2025-04-09T12:48:40.019211Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成角度值\n",
    "theta = np.linspace(0, 2*np.pi, 1000)\n",
    "\n",
    "def plot_unit_circle(p_values, colors, labels):\n",
    "    plt.figure(figsize=(8, 8))\n",
    "    plt.grid(color='gray', linestyle='--', linewidth=0.5)\n",
    "    \n",
    "    for p, color, label in zip(p_values, colors, labels):\n",
    "        if np.isinf(p):\n",
    "            # 处理无穷范数\n",
    "            x = np.cos(theta)\n",
    "            y = np.sin(theta)\n",
    "            x /= np.maximum(np.abs(x), np.abs(y))\n",
    "            y /= np.maximum(np.abs(x), np.abs(y))\n",
    "        else:\n",
    "            # 通用Lp范数计算\n",
    "            x = np.cos(theta)\n",
    "            y = np.sin(theta)\n",
    "            r = np.power(np.power(np.abs(x), p) + np.power(np.abs(y), p), 1/p)\n",
    "            x /= r\n",
    "            y /= r\n",
    "        \n",
    "        plt.plot(x, y, color=color, label=label)\n",
    "    \n",
    "    plt.xlim(-1.5, 1.5)\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.gca().set_aspect('equal')\n",
    "    plt.legend()\n",
    "    plt.title(\"范数的几何解释 - 单位圆对比\")\n",
    "    plt.show()\n",
    "\n",
    "# 定义要绘制的范数参数\n",
    "p_values = [1, 2, np.inf, 4]  # 最后一个是示例的中间值\n",
    "colors = ['blue', 'green', 'red', 'yellow']\n",
    "labels = ['L1 范数（菱形）', \n",
    "         'L2 范数（圆形）',\n",
    "         'L∞ 范数（正方形）',\n",
    "         'L4 范数（中间形状）']\n",
    "\n",
    "plot_unit_circle(p_values, colors, labels)\n"
   ],
   "id": "ba1333a33335d6e4",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ],
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T06:47:57.127020Z",
     "start_time": "2025-04-18T06:47:57.114025Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "f4913eebfd27772a",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T06:47:57.143020Z",
     "start_time": "2025-04-18T06:47:57.130023Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "9d1753c91e207119",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T06:47:57.159135Z",
     "start_time": "2025-04-18T06:47:57.147026Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "656a57fca32eee2d",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T06:47:57.174678Z",
     "start_time": "2025-04-18T06:47:57.161669Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "bdc970f758b714a2",
   "outputs": [],
   "execution_count": null
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T07:30:21.395464Z",
     "start_time": "2025-04-18T07:30:21.385464Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "# 定义另一个特殊的正交矩阵，由0和1（或-1和0）构成\n",
    "# B = np.array([\n",
    "#     [0, 1],\n",
    "#     [1, 0]\n",
    "# ])\n",
    "\n",
    "B = np.array([\n",
    "    [0, 0, 1],\n",
    "    [0, 1, 0],\n",
    "    [1, 0, 0],\n",
    "])\n",
    "\n",
    "\n",
    "# B = np.array([\n",
    "#     [0, 1, 0],\n",
    "#     [1, 0, 0],\n",
    "#     [0, 0, 1],\n",
    "# ])\n",
    "# \n",
    "# B = np.array([\n",
    "#     [1, 0, 0],\n",
    "#     [0, 1, 0],\n",
    "#     [0, 0, 1],\n",
    "# ])\n",
    "\n",
    "\n",
    "# B = np.array([\n",
    "#     [1, 0, 0],\n",
    "#     [0, 1, 0],\n",
    "#     [0, 0, -1],\n",
    "# ])\n",
    "\n",
    "\n",
    "# 计算矩阵B的转置\n",
    "B_transpose = B.T\n",
    "\n",
    "# 计算矩阵B的逆\n",
    "B_inverse = np.linalg.inv(B)\n",
    "\n",
    "# 检验矩阵B的转置是否等于它的逆\n",
    "is_orthogonal_B = np.allclose(B_transpose, B_inverse)\n",
    "\n",
    "print(\"矩阵B:\\n\", B)\n",
    "print(\"矩阵B的转置:\\n\", B_transpose)\n",
    "print(\"矩阵B的逆:\\n\", B_inverse)\n",
    "print(\"矩阵B是否为正交矩阵:\", is_orthogonal_B)\n"
   ],
   "id": "5ad76b050205b439",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "矩阵B:\n",
      " [[0 0 1]\n",
      " [0 1 0]\n",
      " [1 0 0]]\n",
      "矩阵B的转置:\n",
      " [[0 0 1]\n",
      " [0 1 0]\n",
      " [1 0 0]]\n",
      "矩阵B的逆:\n",
      " [[0. 0. 1.]\n",
      " [0. 1. 0.]\n",
      " [1. 0. 0.]]\n",
      "矩阵B是否为正交矩阵: True\n"
     ]
    }
   ],
   "execution_count": 13
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T07:11:14.764393Z",
     "start_time": "2025-04-18T07:11:14.748389Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "A = np.array([\n",
    "    [1, 2],\n",
    "    [3, 4]\n",
    "])\n",
    "# 逆矩阵\n",
    "A_inverse = np.linalg.inv(A)\n",
    "\n",
    "# 验证是否为逆矩阵\n",
    "is_inverse_A = np.allclose(A @ A_inverse, np.eye(2))\n",
    "\n",
    "print(\"矩阵A:\\n\", A)\n",
    "print(\"矩阵A的逆:\\n\", A_inverse)\n",
    "print(\"矩阵A是否为逆矩阵:\", is_inverse_A)"
   ],
   "id": "f4d651f81866ec64",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "矩阵A:\n",
      " [[1 2]\n",
      " [3 4]]\n",
      "矩阵A的逆:\n",
      " [[-2.   1. ]\n",
      " [ 1.5 -0.5]]\n",
      "矩阵A是否为逆矩阵: True\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-04-18T07:11:39.415801Z",
     "start_time": "2025-04-18T07:11:39.408821Z"
    }
   },
   "cell_type": "code",
   "source": "np.linalg.inv(A_inverse)\n",
   "id": "fecc08a90c1a12eb",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2.],\n",
       "       [3., 4.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 11
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "4fbd50918f210003"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
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 },
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